On formal inverse of the Prouhet-Thue-Morse sequence

Maciej Gawro, Maciej Ulas

Let $p$ be a prime number and consider a $p$-automatic sequence $\mathbf{u}=(u_n{)}_{n\in \mathbb{N}}$ and its generating function $U(X)={\sum }_{n=0}^{\infty }{u}_n{X}^n\in {\mathbb{F}}_p[[X]]$. M…